I can't watch the video, but if there are some blokes around wearing dark business suits, they are plainclothes members of the Swiss Guard (usually their colonel is close to the Pope, he is a big guy with short cropped hair), who are all armed with pistols.
The Swiss Guard doesn't just have ceremonial role, they are responsible for security in the Vatican and provide the Pope's bodyguards.
Two years ago, during their 500th anniversary, German TV showed a documentary about this unit (110 men). They also showed their armoury, where they keep the century old halberds, helmets, breastplates and swords they carry on ceremonial duty. In one corner of this armoury though there was a rack holding lots of Swiss Army SIG assault rifles and pistols. One condition for a man to join the Swiss guard is that he must have finished his Swiss military service (the others are that he must be between 19 and 30 years old, physically in good shape, be a Swiss citizen, a clean police record, be single and be Catholic) , so all of them are trained soldiers.